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(1-1/2)(1-1/3)(1-1/4)...(1-1/9) = 1/9 may i know how this is so?

(1-1/2)(1-1/3)(1-1/4)...(1-1/9) = 1/9


may i know how this is so?

Grade:

2 Answers

AskiitiansExpert Abhinav Batra
25 Points
11 years ago

Dear s adhitya

(1-1/2)(1-1/3)(1-1/4)(1-1/5).....(1-1/9)

=1/2*2/3*3/4*......8/9

=1/9(As the denominator and numerator of two consecutive terms cancel except numerator of first and denominator of last term)

 

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AskIITIANS Expert

Abhinav Batra

Parashara K.V.R
18 Points
9 years ago

(1-1/2)(1-1/3)(1-1/4)......(1-1/9)

=(1/2)(2/3)(3/4)....(7/8)(8/9)

=1/9

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